Due to the large size of 3D medical images and their computed features, a method based on analyzing the feature maps or the predicted segmentation map in their native space is unclear and likely to be ineffective. Instead, we propose computing the spectrum of the feature maps, which we define as the vector of singular values computed using a singular value decomposition (SVD). Consider a test image \(x_i\)  and denote the feature map computed for this image at a certain stage (i.e., layer) of the network with \(F_i \in \mathbb {R}^{w, h, d, n}\) , where \(w, h, d\)  denote the dimensions of the feature map and \(n\)  is the number of features. We reshape \(F_i\)  as \(\mathbb {R}^{whd, n}\)  and compute the SVD of \(F_i\)  as \(F_i= U S V\) , where \(U\)  and \(V\)  are orthonormal matrices and the diagonal matrix \(S\)  contains the singular values of \(F_i\) , which is referred to as its spectrum [1]}. Values of the vector of singular values \(s= \text{diag}(S)\)  depend on the magnitude of the feature values, which in turn depend on the image voxel intensities. Moreover, the spectrum has a very large dynamic range. To eliminate these effects, we take the logarithm of the spectrum \(s\)  and then normalize it so that it has an \(\ell _2\)  norm of unity. We refer to the normalized logarithmic spectrum of the feature maps computed as explained above as “the spectral signature" of the feature maps corresponding to an organ of interest. We still denote this spectral signature with \(s\)  in the following.
